Electric machines are utilized in a wide variety of applications. For example, hybrid/electric vehicles (HEVs) typically include an electric traction drive system that includes an alternating current (AC) electric motor which is driven by a power converter with a direct current (DC) power source, such as a storage battery. Motor windings of the AC electric motor can be coupled to inverter sub-modules of a power inverter module (PIM). Each inverter sub-module includes a pair of switches that switch in a complementary manner to perform a rapid switching function to convert the DC power to AC power. This AC power drives the AC electric motor, which in turn drives a shaft of HEV's drivetrain. Traditional HEVs implement a three-phase pulse width modulated (PWM) inverter module, which drives a three-phase AC machine (e.g., AC motor).
Many modern high performance AC motor drives use the principle of field oriented control (FOC) or “vector” control to control operation of the AC electric motor. In particular, vector control is often used in variable frequency drives to control the torque applied to the shaft (and thus finally the speed) of an AC electric motor by controlling the current fed to the AC electric motor. In short, stator phase currents are measured and converted into a corresponding complex space vector. This current vector can then be transformed to a coordinate system rotating with the rotor of the AC electric motor.
Recently, researchers have investigated the possibility of using multi-phase machines in various applications including hybrid/electric vehicles. Higher-order multi-phase systems are characterized by additional degrees of freedom and better reliability in comparison to conventional three-phase machines, as well as by their enhanced torque producing capability.
As used herein, the term “multi-phase” refers to more than three-phases, and can be used in reference to AC electric machines that have five or more phases. One example of a multi-phase system is a five-phase system that includes a five-phase PWM inverter module that drives one or more five-phase AC machine(s). While the possibility of using five-phase systems in HEVs is being explored, a lot of work remains to be done before these inverter and motor configurations can actually be implemented particularly with respect to vector control techniques used in conjunction with such five-phase systems.
To improve dynamic performance of a multi-phase machine it is desirable to improve or increase the available mechanical torque/power that is generated and output by the multi-phase machine. One way to improve output torque (and hence machine efficiency) is to improve utilization of the inverter output or “phase” voltage that is provided to a multi-phase machine.
It is well-known that addition of odd harmonics of appropriate amplitude to a fundamental wave can improve performance of a multi-phase system. For example, a well-known technique for enhancing the performance of a multi-phase machine and improving its torque producing capability and power output is commonly referred to as “third-harmonic current injection.” In third harmonic current injection, a fundamental current command and its third harmonic are used to generate voltage commands that are supplied to the multi-phase machine. Among other things, third-harmonic current injection can be used to increase the inverter output voltage (or phase voltage) and increase flux per pole of a multi-phase machine.
When the AC machine operates in the field-weakening region (medium and high speed), it operates under voltage constraints. To control the AC machine it is necessary to determine the peak phase voltage magnitude (also referred to as “peak voltage” herein) to ensure that it does not exceed a maximum phase voltage that is available to the AC machine. It is desirable to know what the peak value of the phase voltage (Vph) is with reasonable degree of accuracy in advance of every PWM period (at any electrical position) so that any necessary corrections can be made in advance. Because the phase voltage (Vph) is a sinusoidal waveform, most of the time, the phase voltage (Vph) is not at its peak value, but eventually the summed magnitude (A) will reach its peak value in the time domain. It is noted that when normalized, the peak voltage is commonly referred to as a modulation index.
When only the fundamental voltage is to be controlled, peak phase voltage magnitude can be easily calculated. However, in a multi-phase machine that implements third harmonic current injection, calculation of the peak phase voltage magnitude becomes much more complex since the phase voltage includes both a fundamental component and third harmonic component. During third-harmonic current injection the peak summed magnitude (A) of the fundamental voltage vector (V1, φ1) and the third harmonic voltage vector (V3, φ3) is determined by the equation (1) below.A=V1·cos θe−V3 cos(3θe+Δφ),
where V1 is the fundamental voltage vector magnitude (V1), V3 is the third harmonic voltage vector magnitude (V3), θe is the electrical angular position (θe), Δφ is the voltage angle difference (Δφ) between an angle (φ1) of the fundamental voltage vector and an angle (θ3) of the third harmonic voltage vector (φ1-φ3). The electrical angular position (θe) is a function of rotor position that is not necessarily the rotor position (θr). Rather, the electrical angular position (θ) is equal to the rotor position multiplied by a factor that is the number of machine pole pairs (i.e., θ is equal to P*θ for PM machines, or θ is equal to θ*(θr+slip position) for induction machines. Calculation of the peak summed magnitude (A) of the fundamental voltage vector (V1, φ1) and the third harmonic voltage vector (V3, φ3) requires an iterative sweep of at least 180 degrees of the function in equation (1), using a computation loop that iterates a minimum of 90 times in steps of two degrees or less. Calculating the peak voltage using ninety or more iterative computations is time consuming. In many cases, the time required for the calculation can exceed the time available for running the control loop, which in turn forces a lowering of the PWM switching frequency.
Accordingly, it would be desirable to provide techniques for reducing the time required to determine a peak summed magnitude of a fundamental voltage vector and a third harmonic voltage vector, and eliminate the need for this complex calculation including the iterative aspect of the calculation. It would be desirable to reduce the overall execution time of the control loop and thus allow for the PWM switching frequency to be increased. In this regard, it is desirable to provide methods, systems and apparatus for quickly determining peak summed magnitude of a fundamental voltage vector and a third harmonic voltage vector in a multi-phase system that implements third harmonic current injection. Furthermore, other desirable features and characteristics of the present invention will become apparent from the subsequent detailed description and the appended claims, taken in conjunction with the accompanying drawings and the foregoing technical field and background.